(well, first he had to invent calculus)

- The planets move in elliptical orbits
with sun at one focus.

- The speed at which a planet moves varies along the orgit so that
a line from the sun to the planet sweeps out equal areas in equal times.

- The periods
*P*of the planet's orbits are related to the semimajor axes*a*of their orbits by

In fact, Newton found the constant:

This relation allows one to measure the masses of the Earth, the Sun, other planets, stars ...

We can use this relation to find the mass of a planet if it has a moon (or a space probe) orbiting it. If we know

To get the sum of the masses of the planet ( m

Study hint: These last three formulas are a little complicated. For
our purposes, it is enough to remember Kepler's Third Law, that
*P ^{2} = constant * a^{3}* for all of the planets
in the solar system or (with a different constant) for all of the moons
orbiting Jupiter. Then we need to understand that from the motions
of Jupiter's moons we can find the mass of Jupiter, but I do not
recommend memorizing these three formulas.

ASTR 121 Home Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu